Question

In: Statistics and Probability

5. Samples of sizes 100 and 80 of calculus students were acquired. The students in the...

5. Samples of sizes 100 and 80 of calculus students were acquired. The students in the first sample got into calculus by passing the pre-calculus course. Those in the second sample got in by getting a passing score on a placement test. In the first group, 65 succeeded in calculus. In the second group, 41 succeeded. Without using R find a 95% confidence interval for the difference in the success rates of the two populations.

6. For the same data, find the p-value for a test of the alternative hypothesis that the two success rates are not equal without using R.

7. Repeat problems 5 and 6 using R.

Solutions

Expert Solution


Related Solutions

Listed below are grades for Calculus and Precalculus students. Calculus 95, 87, 55, 88, 79, 80,...
Listed below are grades for Calculus and Precalculus students. Calculus 95, 87, 55, 88, 79, 80, 86, 91, 93, 68, 91, 79, 73, 81, 90, 72, 84 Precalculus 82, 66, 42, 90, 82, 38, 77, 90, 72, 65, 71, 88, 63, 93, 67, 55, 34, 82, 71 find the mean, standard deviation, sample size, claim, Ho, H1, critical value, test statistic and conclusion 3) Test the claim that the majority of Calculus students are passing the class with a C...
Random samples of sizes
Random samples of sizes n1 = 25 and n2 = 20 were selected from populations A and B, respectively. From the samples, the standard deviations were computed to be s1 = 5.2 and s2 = 6.8.a. Do the data provide substantial evidence to indicate the populations have different standard deviations? Use α = .05.b. Estimate the relative sizes of the standard deviations by constructing a 95% confidence interval for the ratio of the standard deviations σ1/σ2.c. The data and populations...
The data below are the final exam scores of 5 randomly selected calculus students and the...
The data below are the final exam scores of 5 randomly selected calculus students and the number of hours they slept the night before the exam. Hours, x 4 6 3 9 3 Scores, y 74 89 69 90 75 a) Draw scatterplot for the data. b) Calculate the linear correlation coefficient to 3 decimal places. (if you are unable to calculate the linear correlation coefficient, use .9 for part c,d and e) c) Is there a linear relationship between...
Independent random samples of sizes n1 = 307 and n2 = 309 were taken from two...
Independent random samples of sizes n1 = 307 and n2 = 309 were taken from two populations. In the first sample, 92 of the individuals met a certain criteria whereas in the second sample, 108 of the individuals met the same criteria. Test the null hypothesis H0:p1=p2versus the alternative hypothesis HA:p1<p2. a)  Calculate the z test statistic, testing the null hypothesis that the population proportions are equal. Round your response to at least 3 decimal places.      b) What is the...
Q2) Independent random samples of sizes n1 = 208 and n2 = 209 were taken from...
Q2) Independent random samples of sizes n1 = 208 and n2 = 209 were taken from two populations. In the first sample, 172 of the individuals met a certain criteria whereas in the second sample, 181 of the individuals met the same criteria. Test the null hypothesis H0:p1=p2versus the alternative hypothesis HA:p1>p2. a) Calculate the z test statistic, testing the null hypothesis that the population proportions are equal. Round your response to at least 2 decimal places. b) What is...
(S 11.1) Random samples of sizes n1 = 404 and n2 = 310 were taken from...
(S 11.1) Random samples of sizes n1 = 404 and n2 = 310 were taken from two independent populations. In the first sample, 107 of the individuals met a certain criteria whereas in the second sample, 135 of the individuals met the same criteria. Run a 2PropZtest to test whether the proportions are different, and answer the following questions. What is the value of p?, the pooled sample proportion?Round your response to at least 3 decimal places. Calculate the z...
Independent random samples of sizes n1 = 202 and n2 = 210 were taken from two...
Independent random samples of sizes n1 = 202 and n2 = 210 were taken from two populations. In the first sample, 170 of the individuals met a certain criteria whereas in the second sample, 178 of the individuals met the same criteria. Test the null hypothesis H0:p1=p2versus the alternative hypothesis HA:p1>p2. a)  Calculate the z test statistic, testing the null hypothesis that the population proportions are equal. Round your response to at least 3 decimal places.      b) What is the...
One hundred blood samples were taken from 100 individuals. All of the blood samples were run...
One hundred blood samples were taken from 100 individuals. All of the blood samples were run through two machines to determine if the machines were testing samples appropriately. We expect that both machines should yield similar results. Below are the results of the analysis. Assume there are 100 sample and they are normal. Are the two machines similar? Should we check into whether one machine should be replaced? Show all of your work. Beckman Machine Coulter Machine 3. 4. 5....
Consider the following means and sample sizes for two independent samples (with the samples being denoted...
Consider the following means and sample sizes for two independent samples (with the samples being denoted by the subscripts "X" and "Y"): MX = 6.286, MY= 1.973, nX= 16, nY= 16. If the standard error (sDifference) is 2.256, what is the the upper boundary of the corresponding 95% confidence interval? Please use a typical null hypothesis that predicts no differences between the two populations when computing your answer. When calculating your answer, please ensure that you subtract the mean for...
Two random samples of 40 students were drawn independently from two populations of students. Assume their...
Two random samples of 40 students were drawn independently from two populations of students. Assume their aptitude tests are normally distributed (total points = 100). The following statistics regarding their scores in an aptitude test were obtained: xbar1= 76, s1 = 8, xbar2 = 72, and s2 = 6.5. Test at the 5% significance level to determine whether we can infer that the two population means differ. (Note: You cannot necessarily assume that the populations have the same variances). Please...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT